The objective of this grant is to develop recent theoretical advances in mathematical statistics for use in medical applications. This includes the theoretical study of these new ideas and their adaptation for use in a medical setting. It also requires testing their validity and worth on real data, and expositing the results in a fashion understandable to practicing biostatisticians. At the outset three principal areas (censored data, empirical Bayes, and robust methods) were singled out for special consideration, but attention is not necessarily restricted to them. A number of on-going projects at the Stanford Medical School (heart transplant program, operating room trace gas study, etc.) provide excellent data bases for testing these new techniques.